Complexity results on a paint shop problem
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Paintshop, odd cycles and necklace splitting
Discrete Applied Mathematics
Greedy colorings for the binary paintshop problem
Journal of Discrete Algorithms
Complexity results on restricted instances of a paint shop problem for words
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Approximation algorithms for the Bipartite Multicut problem
Information Processing Letters
Computing solutions of the paintshop-necklace problem
Computers and Operations Research
Note: Greedy colorings of words
Discrete Applied Mathematics
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In the binary paint shop problem we are given a word on n characters of length 2n where every character occurs exactly twice. The objective is to colour the letters of the word in two colours, such that each character receives both colours and the number of colour changes of consecutive letters is minimized. Amini et al. proved that the expected number of colour changes of the heuristic greedy colouring is at most 2n/3. They also conjectured that the true value is asymptotically n/2. We verify their conjecture and, furthermore, compute an expected number of (2n+1)/3 colour changes for a heuristic, named red first, which behaves well on some worst case examples for the greedy algorithm. From our proof method, finally, we derive a new recursive greedy heuristic which achieves an average number of 2n/5+O(1) colour changes.